In this paper, homotopy perturbation method (HPM) is applied to solve fractional partial
differential equations (PDEs) with proportional delay in t and shrinking in x. The method do …

Separation of Variables and Exact Solutions to Nonlinear PDEs is devoted to describing and
applying methods of generalized and functional separation of variables used to find exact …

We present a new method for constructing exact solutions of nonlinear delay PDEs using
special solutions of simpler auxiliary PDEs without delay. The application of the method is …

For the first time, the general nonlinear Schrödinger equation is investigated, in which the
chromatic dispersion and potential are specified by two arbitrary functions. The equation in …

In the present article, fractional-order partial differential equations with proportional delay,
including generalized Burger equations with proportional delay are solved by using Natural …

The paper deals with different classes of non-linear reaction–diffusion equations with
variable coefficients c (x) ut=[a (x) f (u) ux] x+ b (x) g (u), that admit exact solutions. The direct …

A novel collocation method based on Genocchi wavelet is presented for the numerical
solution of fractional differential equations and time‐fractional partial differential equations …

The paper deals with one-dimensional nonlinear delay reaction–diffusion equations with
varying transfer coefficients of the form ut=[G (u) ux] x+ F (u, u ̄), where u= u (x, t) and u ̄ …

The paper presents a number of new functional separable solutions to nonlinear reaction–
diffusion equations of the form c (x) ut=[a (x) ux] x+ b (x) u x+ p (x) f (u), where f (u) is an …

We present a number of new generalized separable, functional separable, periodic and
antiperiodic exact solutions to non-linear delay reaction–diffusion equations of the form ut …